REVIEW SUMMARY◥

MEMBRANES

Maximizing the right stuff: Thetrade-off between membranepermeability and selectivityHo Bum Park, Jovan Kamcev, Lloyd M. Robeson,Menachem Elimelech, Benny D. Freeman*

BACKGROUND: Synthetic membranes areused for desalination, dialysis, sterile filtra-tion, food processing, dehydration of air andother industrial, medical, and environmentalapplications due to low energy requirements,compact design, and mechanical simplicity.New applications are emerging from the water-energy nexus, shale gas extraction, and en-vironmental needs such as carbon capture.All membranes exhibit a trade-off betweenpermeability—i.e.,howfastmoleculespass througha membrane material—and selectivity—i.e., towhat extent the desired molecules are sepa-rated from the rest. However, biological mem-branes such as aquaporins and ion channelsare both highly permeable and highly selective.Separation based on size difference is common,but there are other ways to either block onecomponent or enhance transport of another

through a membrane. Based on increasingmolecular understanding of both biologicaland synthetic membranes, key design criteriafor new membranes have emerged: (i) prop-erly sized free-volume elements (or pores), (ii)narrow free-volume element (or pore size) dis-tribution, (iii) a thin active layer, and (iv) highlytuned interactions between permeants of in-terest and themembrane. Here, we discuss thepermeability/selectivity trade-off, highlight sim-ilarities and differences between synthetic andbiological membranes, describe challenges forexistingmembranes, and identify fruitful areasof future research.

ADVANCES: Many organic, inorganic, and hy-brid materials have emerged as potential mem-branes. In addition to polymers, used for mostmembranes today, materials such as carbon

molecular sieves, ceramics, zeolites, various nano-materials (e.g., graphene, graphene oxide, andmetal organic frameworks), and their mixtureswithpolymershavebeenexplored.Simultaneously,global challenges such as climate change and

rapid population growthstimulate the search forefficientwaterpurificationandenergy-generationtech-nologies, many of whicharemembrane-based. Ad-ditional driving forces in-

cludewastewater reuse from shale gas extractionand improvementof chemical andpetrochemicalseparation processes by increasing the use oflight hydrocarbons for chemicalsmanufacturing.

OUTLOOK:Opportunities for advancingmem-branes include (i) more mechanically, chem-ically, and thermally robust materials; (ii)judiciously higher permeability and selec-tivity for applications where such improve-ments matter; and (iii) more emphasis onfundamental structure/property/processingrelations. There is a pressing need for mem-branes with improved selectivity, rather thanmembranes with improved permeability, es-pecially for water purification. Modeling at alllength scales is needed to develop a coherentmolecular understanding of membrane prop-erties, provide insight for future materialsdesign, and clarify the fundamental basisfor trade-off behavior. Basic molecular-levelunderstanding of thermodynamic and diffu-sion properties of water and ions in chargedmembranes for desalination and energy ap-plications such as fuel cells is largely incom-plete. Fundamental understanding ofmembranestructure optimization to control transportof minor species (e.g., trace-organic contam-inants in desalination membranes, neutralcompounds in chargedmembranes, and heavyhydrocarbons in membranes for natural gasseparation) is needed. Laboratory evaluationof membranes is often conducted with highlyidealized mixtures, so separation performancein real applications with complex mixtures ispoorly understood. Lack of systematic under-standing of methodologies to scale promisingmembranes from the few square centimetersneeded for laboratory studies to the thousandsof square meters needed for large applicationsstymies membrane deployment. Nevertheless,opportunities for membranes in both existingand emerging applications, together with anexpanding set of membrane materials, holdgreat promise for membranes to effectivelyaddress separations needs.▪

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Author affiliations are available in the full article online.*Corresponding author. Email: freeman@che.utexas.eduCite this article as H. B. Park et al., Science 356, eaab0530(2017). DOI: 10.1126/science.aab0530

From intrinsic permeability/selectivity trade-off to practical performance in membranes.Polymer membranes for liquid and gas separation applications obey a permeability/selectivitytrade-off—highly permeable membranes have low selectivity and vice versa—largely due tobroad distributions of free-volume elements (or pores in porous membranes) and nonspecificinteractions between small solutes and polymers.We highlight materials approaches to overcomethis trade-off, including the development of inorganic, isoporous, mixed matrix, and aquaporinmembranes. Further, materials must be processed into thin, typically supported membranes,fashioned into high surface/volume ratio modules, and used in optimized processes. Thus, factorsthat govern the practical feasibility of membranes, such as mechanical strength, module design,and operating conditions, are also discussed.

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REVIEW◥

MEMBRANES

Maximizing the right stuff: Thetrade-off between membranepermeability and selectivityHo Bum Park,1 Jovan Kamcev,2 Lloyd M. Robeson,3

Menachem Elimelech,4 Benny D. Freeman2*

Increasing demands for energy-efficient separations in applications ranging from waterpurification to petroleum refining, chemicals production, and carbon capture havestimulated a vigorous search for novel, high-performance separation membranes. Syntheticmembranes suffer a ubiquitous, pernicious trade-off: highly permeable membranes lackselectivity and vice versa. However, materials with both high permeability and highselectivity are beginning to emerge. For example, design features from biological membraneshave been applied to break the permeability-selectivity trade-off.We review the basis for thepermeability-selectivity trade-off, state-of-the-art approaches to membrane materialsdesign to overcome the trade-off, and factors other than permeability and selectivity thatgovern membrane performance and, in turn, influence membrane design.

Synthetic membranes, based largely onpolymers, are widely used in gas separa-tions (e.g., air dehydration; O2/N2 separa-tion; hydrogen purification; and CO2, H2S,and higher hydrocarbon removal from natu-

ral gas), water purification (e.g., desalination, ultra-pure water production, drinking water treatment,and municipal and industrial wastewater treat-ment and reuse) (1–3), bioprocessing (e.g., sterilefiltration, protein concentration, and buffer ex-change) (4, 5), medical applications (e.g., dialy-sis, blood oxygenation, and drug delivery) (6),food processing (e.g., beer and wine clarificationand demineralization of whey, juices, and sugar)(7, 8), chemicals production (e.g., chlor-alkali pro-cess to produce chlorine and sodium hydroxide)(8), batteries (9), and fuel cells (10, 11). Potentialapplications include energy generation (12, 13);energy storage (14); environmental applicationssuch as carbon capture (15) and selective removalof ions (e.g., nitrates and phosphates) contributingto surface water eutrophication (16); organicsolvent recovery (17); pharmaceutical purification(18); catalyst recovery (18); and membrane crys-tallization (19), distillation (3, 19), and emulsifi-cation (20). In many applications, membranesare favored over other processes due to advan-tages in energy efficiency, simplicity, manufactur-

ing scalability, and small footprint (1–3). However,all synthetic membranes are subject to a trade-offbetween permeability and selectivity, as well aspractical challenges such as fouling, degrada-tion, and material failure that limit their use.

Origin of the permeability-selectivitytrade-off

The commercialization of polymeric membranesfor gas separations in the late 1970s catalyzed asustained search for materials with better sepa-ration properties. As the database of gas per-meation properties on various materials expanded,researchers discovered a trade-off between gaspermeability, Pi (see Box 1 for definition), andselectivity, ai,j = Pi /Pj, where i represents themore permeable gas of the i, j gas pair (e.g., i =O2 and j = N2 in air separation) (21). During the1980s, permeability data on six common gases(He, H2, O2, N2, CO2, and CH4) were compiled,and the trade-off relationship between perme-ability and selectivity was analyzed. Polymershaving the highest selectivity at a given perme-ability lay near or on a line, called the upperbound, obeying the following relation (21)

ai;j ¼ bi;jP�li;ji ð1Þ

where li,j and bi,j are parameters depending onthe gas pair. An example for air separation (i.e.,O2/N2 separation) is shown in Fig. 1A. More per-meable polymers tend to have lower selectivity,and vice versa. This study (21) became the stan-dard against which permeability and selectivityvalues for new and improved membrane mate-rials were measured.A theoretical model of the permeability/

selectivity trade-off (22) revealed that the slope,

li, j, depends on the ratio of gas molecule di-ameters, li, j = (dj/di)

2 − 1, where dj and di arethe kinetic diameters of the larger and smallergases, respectively, and upper-bound behaviorwas found for all gas pairs reported. The frontfactor, bi, j, depends on gas solubility, li, j, and anadjustable constant, f, related to the average dis-tance between polymer chains and chain stiffness.This model was based on five hypotheses: (i) gaspermeation occurs via the solution-diffusion mech-anism (see Box 1); (ii) gas diffusion is an activatedprocess, described by an Arrhenius equation;(iii) the activation energy of diffusion, ED, ofa gas molecule depends on the square of itseffective size; (iv) a universal linear free-energyrelation exists between ED and the front factorin the Arrhenius equation; and (v) gas solubilitydepends on gas molecule condensability, as ex-pressed, for example, by the Lennard-Jones welldepth of the gas molecule.The 1991 upper-bound results (21) were re-

visited in 2008 with a much larger database andnotable advances in the search for more per-meable and selective polymers (23). In most cases,only modest shifts in the upper bound wereobserved despite many studies between 1991and 2008 aimed at preparing materials to exceedthe upper bound. This point is illustrated in Fig.1A where the 1991 and 2008 upper bounds aresuperimposed. Notably, and in agreement withthe upper-bound model (22), the slopes, li, j, ofthe upper bound did not change, but the posi-tion of the upper bound, bi, j, moved as shownin Fig. 1A for all gas pairs considered.The most significant changes in bi, j values

were with He-based gas pairs (specifically He/H2),where glassy perfluorinated polymers came todominate the upper bound (23). Perfluoropolymersexhibit unique gas solubility characteristics rela-tive to aromatic and other hydrocarbon polymers,for reasons still unresolved at a fundamental level(24, 25). These solubility characteristics accountfor the presence of perfluoropolymers at the up-per bound for some gas pairs.For other gas pairs, bi, j values changed due to

introduction of newmaterials. Two classes of poly-mers—PIMs (polymers of intrinsicmicroporosity,e.g., polybenzodioxanes) (26) and TRs (thermallyrearranged polymers, e.g., polybenzoxazoles)(27)—gave exceptional performance. For CO2/CH4,several TR polymers significantly exceeded the up-per bound. The bases for their unusually highpermeability/selectivity combinations are (i) highgassolubility, an inherent characteristic of high free-volume glassy polymers such as PIMs and TRpolymers; (ii) high gas diffusion coefficients,which are also a consequence of high free vol-ume; and (iii) for several gas pairs (e.g., O2/N2

and CO2/CH4), unusually high gas diffusion se-lectivity, suggesting size and size distributionof free-volume elements in a range particularlysuitable for separating these gasmolecules basedon sub-Angstrom differences in effective gasmol-ecule size (28).A comparison of rubbery versus glassy (i.e.,

flexible versus rigid) polymers (29) revealed thatgas solubilities are uniformly higher in glassy

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1Department of Energy Engineering, Hanyang University,Seoul 04763, Republic of Korea. 2Department of ChemicalEngineering, Texas Materials Institute, Center for Research inWater Resources, and Center for Energy and EnvironmentalResearch, The University of Texas at Austin, 10100 BurnetRoad, Building 133 (CEER), Austin, TX 78758, USA.3Department of Materials Science and Engineering, LehighUniversity, 1801 Mill Creek Road, Macungie, PA 18062, USA.4Department of Chemical and Environmental Engineering,Yale University, New Haven, CT 06520-8286, USA.*Corresponding author. Email: freeman@che.utexas.edu

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than rubbery polymers when compared at equiv-alent permeabilities, due to additional sorptionof gas into the nonequilibrium excess volumeinherently present in glassy polymers (i.e., dual-mode sorption) (30). Thus, glassy polymers dom-inate the upper bound mainly due to higher gassolubility than rubbery polymers (29). Whencompared at equivalent free-volume levels, rub-bery and glassy polymers have very similar dif-fusion selectivities (29). That is, for most polymers,diffusion selectivity differences between glassyand rubbery polymers only modestly favor glassypolymers, in contrast to generalizations previouslyreported and accepted in the literature.Various approaches to exceed the upper bound

have been explored, including surface modifica-tion (31, 32), facilitated transport (33), phase-separated polymer blends (34), andmixed-matrixmembranes (MMMs) (35). Although the upper-boundconcept as originally formulatedonly appliesto homogeneous polymer membranes, compar-ing permeability and selectivity data on upper-bound plots remains a popular way to gaugemembrane material performance. In additionto the upper-bound pairs possible from the sixgases noted above, upper-bound relationshipshave been reported for other important gas pairs,such as propylene/propane (36), ethylene/ethane(37), and N2/NF3 (38).Other examples of such trade-off behavior

have emerged in virtually all synthetic polymermembranes, including desalination membranes(39) (Fig. 1B), forward osmosis membranes (40–42),porous ultrafiltration (UF) membranes (43) (Fig.1C), polymer electrolyte membranes for fuel cells(44) (Fig. 1D), pervaporation membranes (45),and ion-exchange membranes (46). The funda-mental physics of small-molecule transport throughdense, nonporous polymers (e.g., for gas separationand water/salt separation (47)) are different fromthose of proteins through porous UF membranesand ion transport through charged polymersin electrically driven separations (3, 5, 8, 43).Nevertheless, upper-bound behavior is observedin all cases, suggesting the generality of thisphenomenon in both dense and porous mem-branes. Additionally, materials used to formeither porous or dense membranes do not nec-essarily have to be polymeric for the resultingmembranes to exhibit permeability-selectivitytrade-offs (48).Common features of the dense polymer mem-

branes mentioned above are a broad distributionof free-volume element sizes, as shown in Fig. 2,A and B, and relatively nonspecific interactionsgoverning solubility of small molecules in poly-mers (3, 27, 30). Changing a polymer structureto give more rapid permeation often enhancespermeability of larger species more than smallerspecies, resulting in increased permeability butdecreased selectivity. This pattern has been as-cribed to a lack of ability to increase free-volumeelement size while simultaneously narrowingfree-volume element size distribution (27). Mem-branes with very narrow pore size distributionsare “isoporous” membranes (i.e., those with uni-form pore sizes), as shown in Fig. 2, C and D. Such

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Box 1. Solution-diffusion transport mechanism in nonporous polymers. Gas permeabilityis defined as Pi = NiL/Dp, where Ni is the steady-state flux of gas i through the membrane,L is membrane thickness, and Dp is the transmembrane pressure difference (or partial pressuredifference, in the case of gas mixtures). The three-step solution-diffusion mechanism isthe accepted framework for small-molecule transport in nonporous polymers (120). A penetrantmolecule (i) dissolves into the upstream (i.e., high concentration) side of a membrane, (ii) diffusesthrough the membrane, and (iii) desorbs from the downstream (i.e., low concentration) sideof a membrane. The second step is the rate-limiting step in all current membranes, and therate-limiting step in gas diffusion through polymers is the local segmental dynamics of thepolymer chains, which open transient gaps (i.e., free-volume elements) through which gasdiffusion occurs. In this framework, permeability is written as Pi = SiDi, where Si and Di arethe penetrant solubility and diffusivity in the polymer, respectively, and ai,j = (Si/Sj) × (Di/Dj),where Si/Sj and Di/Dj are the solubility and diffusivity selectivities, respectively. The samemechanism applies to water and salt transport in RO membranes and other membraneprocesses involving nonporous materials (120). The gas permeability unit is the barrer, where

1 barrer ¼ 10�10 cm3ðSTPÞ cmcm2 s cmHg . Gas flux is often normalized by pressure to give permeance, Pi /L =

Ni/Dp, which is reported in gas permeation units (GPU), where 1 GPU ¼ 10�6 cm3ðSTPÞcm2 s cmHg. In

RO desalination membranes, the equivalent expression for water flux, Nw, is Nw = A(Dp – Dp),

where A (i.e., permeance) contains the membrane permeability to thickness ratio, Dp is theapplied hydrostatic pressure, and Dp is the osmotic pressure difference across the membrane,generated by the difference in salt concentration on either side of the membrane (121).

Fig. 1. Upper-bound relations in polymer membranes. (A) O2/N2 separation (23); (B) water/saltseparation (39); (C) protein/water separation in porous ultrafiltration membranes [1/Sa is theseparation factor of bovine serum albumin (BSA) from water and other small solutes (e.g., salts andsugars)], and hydraulic permeability is the rate of transport through the membrane of water andany solutes not retained by the membrane (43); and (D) polymer electrolyte membranes, where ionicconductivity for membranes at a given level of water uptake (i.e., water sorption) is apparentlylimited by an upper-bound type relationship (44).

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membranes can have both high permeabilityand high selectivity because the isoporous geome-try contributes to membranes with no tortuosity(high permeability) and precise, uniform poresize (high selectivity). However, practical devel-opment of these membranes is in its infancy.

Design approaches for improvedpermeability and selectivity

Biological membranes, such as potassium ionchannels and aquaporins (Fig. 2, E and F), haveextremely high selectivity-permeability combina-tions, which has stimulated recent efforts aimedat (i) direct incorporation of such structures intomembranes (49), (ii) theoretical studies aimed atunderstanding optimal structures (Fig. 2G) thatmight yield high permeability and selectivity, or(iii) synthetic membrane structures that mimicor are inspired by one or more elements of bi-ological membranes. So far, incorporation of, forexample, aquaporins into membranes has beendone via assimilation of aquaporins into vesiclesand integration of the resulting vesicles intomembranes, but there are no successful, repro-ducible studies demonstrating that this strategycan produce highly selective membranes (48).Thus, much remains uncertain about their abilityto be processed into the large-scale, defect-freestructures required for practical applications orwhether they can maintain adequate transportand selectivity properties upon exposure to com-plex, real-world feed mixtures for extended periodsof time. We return to these points below.Certain structural changes in polymers used

for gas separation, such as thermal rearrange-ment, narrow an otherwise broad free-volumeelement size distribution. This contributes tohigher permeability-selectivity combinations, butsuch materials still have a wide distribution offree-volume elements relative to biological mem-branes (27). Block copolymers innately self-assembleinto well-defined structures with regular perio-dicity. This phenomenon has been harnessed toprepare ~15-nm-diameter isoporous membraneswith complete rejection of virus particles andhigh water flux (50). This concept was extendedto prepare isoporous UF membranes via non-solvent-induced phase inversion (NIPS), an in-dustrial process used to produce many currentmembranes, providing a potential route to large-scale production of such structures (51). Optimi-zation of this process led to water permeancesof 3200 L m−2h−1bar−1, an order of magnitudehigher than conventional NIPS membranes ofthe same average pore size, coupled with a se-lectivity of 87 for separating bovine serum albumin(MW = 67 kDa, diameter ~6.8 nm) from globulin-g(MW = 150 kDa, diameter ~14 nm), proteins tooclose in size to be separated by conventional UFmembranes (52). The high water permeance insuch isoporous membranes was due to higherporosity and lower tortuosity at similar pore sizerelative to conventional UF membranes. Typically,such self-assembled structures can be used to makeisoporous membranes with pore sizes rangingfrom 3 to 20 nm, in the range of UF membranes.Using mixtures of different block copolymers,

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Fig. 2. Evolution of cavity (or pore) size distributions in membranes. Cavity (or pore) sizedistributions in separation membranes, ranging from (A) broad cavity-size distributions in densepolymers, such as those used in gas separations (113) and (B) water purification (e.g., porousultrafiltration membranes) (114) to narrow pore size distributions in (C) isoporous UF membranesformed via self-assembly of block copolymers (~34-nm pore diameter) (52), (D) graphenenanomesh having ~30-nm pores prepared via block copolymer lithography (115), (E) potassium ionchannel (116), (F) aquaporin (93), and (G) the effect of hourglass pore design parameters (poreopening angle, a, and aspect ratio, L/a) on water permeability (117).

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the pore size was reduced to ~1.5 nm, whilestill maintaining high water flux (53), yieldingnanofiltration (NF) membranes, thereby poten-tially opening a large set of practically importantseparations (e.g., dye removal from textile waste-water). The detailed formation mechanism ofsuch membranes is still under debate (54). Blockcopolymers, such as those used to prepare theoriginal isoporous membranes, are expensiverelative to traditional polymers used in water-purification membranes. If isoporous membranewere made entirely of such block copolymers,cost would likely be a considerable roadblock forsuch materials, restricting their use to high-value,low-volume separations (e.g., biomedical applica-tions) rather than large-scale drinking or waste-water purification applications.Inorganic materials offer efficient ways to

tailor pore sizes and shapes and achieve narrowpore size distributions, potentially leading to highpermeability and/or high selectivity. For example,metal-organic frameworks (MOFs) have beenstudied for gas separation and other relatedapplications (55). MOFs are synthesized by con-necting inorganic and organic units via covalentbonds to form permanently porous crystallinestructures. Numerous MOFs with various well-defined pore sizes and channels have been reported(56). Due to their high porosity (~50% of thecrystal volume); high surface area (~10,000 m2g−1),which exceeds traditional inorganic materials(e.g., zeolites and carbon molecular sieves); andextensive ability to chemically tailor MOFs, theyhave been widely studied as membrane mate-rials. Crystalline MOF membranes on poroussubstrates have been explored, particularly forgas separation applications. Like zeolite mem-branes, continuous MOFmembranes are preparedprimarily by in situ and seeded-secondary growthmethods. More recently, zeolitic imidazole frame-works (ZIFs), a subclass of MOFs, have been ofinterest for gas separations, mainly because theirpore size is similar to the size of small gas mol-ecules and they can exhibit high chemical andthermal stability (57, 58).Although continuous, self-supporting thin films

of MOFs would be preferred for membrane ap-plications, they arenotmechanically robust enoughto form large surface area membranes. Conse-quently, they are fabricated onmechanically stableporous supports (58). Additionally, such crystallinematerials in the thin-film state contain intrinsic orextrinsic defects (e.g., grain boundaries) betweensingle crystalline domains, leading to nonselectiveflow (59). Many studies focus on minimizing suchdefects to achieve high selectivity and reducing thethickness of the active layer to achieve high per-meance. For example, Nair and colleagues. coatedZIF-8 onto polymeric hollow fibers using two-solvent interfacial synthesis (58). They used highlygas-permeable, porous poly(amide-imide) hollowfibers as a support andprepareda continuousZIF-8membrane on the lumen surface of the hollowfibers via interfacial microfluidic membrane pro-cessing. Thesemembranes showed clearmolecularsieving properties—highH2 permeance [3000 gaspermeation units (GPU)], high H2/C3H8 selectiv-

ity (130 at 120°C), and a strong temperature de-pendence of H2 permeance, implying activatedmolecular transport through the ZIF-8 pores.Whendefects were sealed with poly(dimethylsiloxane),the H2/C3H8 selectivity increased to 370, but H2

permeance decreased to 750 GPU. ZIF-8 has aneffective aperture (i.e., pore) size of ~4.0 Å, so itmay be of interest for propylene/propane separa-tion, a large-scale, highly energy-intensive sepa-ration (36). More recently, Kwon et al. reportedheteroepitaxially grownZIFmembranes consistingof two different ZIF layers (60). Submicrometer-thick ZIF-67 membranes were heteroepitaxiallygrown from ZIF-8 seed layers on alumina sup-ports. Addition of a ZIF-8 overlayer (~300 nm)on a ZIF-67membrane led to very high propylene/propane separation factor (~200) with high pro-pylene permeability, well above the upper boundfor both polymer and carbon membranes (36).However, since alumina is a brittle ceramic, thisapproach does not solve the basic mechanicalproperty challenge facing such materials, ren-dering scale-up of these membranes unlikely.Grapheneandother two-dimensional (2D) atom-

ically thin materials (e.g., graphdiyne, graphyne,hBN, andMoS2, 2D polymers based on polypheny-lene, porphyrin, and cyclohexa-m-phenylene, etc.)have attracted attention because of the minimumpossible thickness, high mechanical strength,chemical stability, and ability to create selec-tive nanoscale pores in their rigid 2D lattices(61). Two distinct strategies to use suchmaterials(e.g., graphene) formembranes have been reported:(i) creating nanopores (or defects) in the basal plane(62) or (ii) tailoring the 2Dnanochannels inherentlypresent between stacked 2D sheets (e.g., grapheneoxide or reduced graphene oxide) (63). Simulationssuggest that monolayer porous graphene could behighly permeable and selective, with higher separa-tion performance than polymermembranes. Gasseparation and water/ion separation propertieshave beenmeasured using such porous graphenemembranes (62, 64). Precisely tuning the nano-channels between stacked 2D graphene sheets,or controlling the pore size and achieving highporosity with large-area graphene membranes,pose considerable technological challenges due todefect control in raw graphenemonolayers. There-fore, such materials cannot be used for industrial,large-areamembraneswithoutmajorbreakthroughsin large-scale, reproducible manufacturing.As an example of the properties of such ma-

terials, Surwade et al. created small nanopores(~1 nm) via oxygen plasma irradiation at a densityof ~1012 cm−2 in monolayer graphene membranesplaced on a microscale aperture. The resultingmembranes exhibited high water permeability(64). In one sample, the driving force normalizedwater flux (i.e., permeance) was 250 Lm−2h−1bar−1,whereas a state-of-the-art reverse osmosis (RO)membrane would have a permeance of about2.3 L m−2h−1bar−1 (65–68). However, this per-forated graphene membrane had poor salt/waterselectivity, ranging from about 5 to 200 (the widerange presumably due to sample-to-sample vari-ability). For comparison, a state-of-the-art ROmembrane requires a salt/water selectivity of

16,000 to meet water purity requirements, andaquaporins have essentially infinite selectivityand a permeance of 1.6 × 106 L m−2h−1bar−1 peraquaporin (68).Graphene oxide (GO) has a high density of

oxygen-containing functional groups (e.g., hydroxyl,epoxy, and carboxyl) and some vacancy defectsin the 2D carbon lattice. GO can be preparedinexpensively on a large scale by oxidation andexfoliation of graphite. GO sheets can be readilydispersed in water or organic solvents, providingfacile means for membrane fabrication via well-developed membrane-coating technology usingGO dispersions (69, 70). Differing from nano-porous graphene, adjustable 2D nanochannelsbetween adjacent GO sheets can be used forselective molecular transport. GO membranescan have high water-transport rates (71), becausethe oxidized domains act as spacers to separateadjacent GO sheets and facilitate water moleculeintercalation, and the pristine graphitic domainsin GO sheets create a network of capillaries allow-ing almost frictionless flow of water, similar towater transport through carbon nanotubes (72).In addition, GO membranes can display sievingproperties in aqueous solutions (69), blockingall solutes with hydrated radii larger than 0.45 nm,which is inadequate for desalination applications,given that, for example, a hydrated sodium ionis smaller than this.GO membranes have also been explored for

gas separations. Li et al. (73) fabricated ultrathinGO membranes (e.g., ~1.8 nm thick) that exhibitedhigh H2/CO2 and H2/N2 selectivity. Kim et al. (63)demonstrated that hydrated thin GO membranescan be used as CO2-selective membranes becausepermeance of all gases, except CO2, decreasedas feed humidity increased. Condensed watermolecules in the pores, or between GO sheets,hindered transport of relatively noncondensablesmall molecules such as N2. As with grapheneand other 2D atomically thin materials discussedbefore, fabrication of defect-free, large-scale GOmembranes for liquid or gas separation is ex-tremely challenging, due to their poor mechanicalproperties, which markedly limits the practicalityof such membranes.On the laboratory scale, a 10 cm2 (10−3 m2)

membrane sample is often sufficient to generateinitial characterization data. However, industrialproduction of membranes for large-scale appli-cations can require 1000 to 100,000 m2 of mem-branes, all of which must be prepared with defectdensities, for gas separations, below about 1 cm2

of defects for every 105 cm2 of membrane surfacearea (74, 75). Such a 106 to 108 scale-up in the sizeof defect-free membranes is often a major stumbl-ing block for introduction of new materials asmembranes and is exacerbated if the new materialscannot be readily transformed into thin, defect-free membranes using conventional membrane-formation methods (3).One popular approach to address difficulties

in preparing large-surface-area, defect-free, ultra-thinmembranes of promising nanomaterials (e.g.,carbon nanotubes, graphene, zeolites, and MOFs)is the use of mixed-matrix membranes (MMMs).

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MMMs commonly consist of a dispersed nano-material phase and a continuous polymermatrix,hoping to marry the high intrinsic permeabilityand separation properties of advanced nano-materialswith the robust processing andmechan-ical properties of polymers (Fig. 3). Most studiesinvolving MMMs have focused on gas separationmembranes (76), in which molecular sieving par-ticles such as zeolites, carbons, and MOFs havebeen incorporated into a polymer matrix to altertheir performance. More recently, nanotubes andnanosheets have been considered as the dispersedphase (77, 78). Koros and colleagues theoreticallyanalyzed the potential of MMMs, predicting gasseparation performance beyondRobeson’s upperbound (particularly for O2/N2 separation) (35).However, most experimental results fall belowthe theoretical maximum because of unfavorablylarge interfacial gaps between the dispersednanomaterials and polymermatrix and relativelylimited dispersed phase loading due to particleagglomeration (79). As such, much of the effortto enhance separation performance in MMMsfocuses on reducing the incompatibility betweeninorganic materials and organic polymers, whileachieving homogeneous dispersions at high load-ing levels (80, 81). However, despite well over adecade of sustained efforts to develop large-scale,practical MMMs, there are no commercial ex-amples of such membranes. Uniformly dispers-ing nanomaterials in thin polymer selective layers(e.g., <100 nm thick) via continuous processes(e.g., hollow fiber spinning) tomake reproducible,large-surface-area membranes, without introduc-ing selectivity-destroying defects while maintain-ing sufficient mechanical properties to permitmanufacturing and use of the resulting mem-branes, has proven an arduous undertaking dueto the large number of processing variables affect-ing the final material structure.In principle, in the absence of significant inter-

facial gaps and with homogeneous dispersion,inclusion of inorganic materials can improvemembrane performance by increasing selectivity,permeability, or both. Interfacial compatibility,interaction energy between nanomaterials andpolymers, type of nanomaterial (e.g., zeolites,silica, carbon molecular sieves, activated carbon,MOFs, carbon nanotubes, metal oxides, meso-porous materials, nonporous materials, and nano-sheets), nanomaterial concentration, orientationof anisotropic nanomaterials, and permeationproperties of the polymer continuous phase allinfluence membrane performance (77, 82, 83).Scalable processing of MMMs is less difficultthan processing membranes made solely fromnovel nanomaterials (e.g., MOFs and carbonnanotubes) but can be much more difficult thanprocessing polymers alone. Successfully includ-ing such nanomaterials into thin, selective poly-mer layers less than 100 nm thick requires smallfiller size. Bachman et al. reported MOF nano-crystals dispersed in a polyimide membrane forolefin/paraffin separation (55). Small MOF nano-crystals (17 to 18 nm), having high external surfacearea, led to a greater fraction of polymer at thepolymer/MOF interface, thereby reducing the

number of nonselective pathways for gas trans-port, resulting in high ethylene/ethane separa-tion performance with increasing MOF content(55). Incorporation of larger MOFs (i.e., 100 to200 nm) did not show performance improve-ment relative to that of membranes containingsmaller MOF nanocrystals.In addition to the factors discussed above, filler

shape and orientation are important. Anisotrop-ically shaped (e.g., sheetlike) inorganic materialsmay be better than isotropically shaped materialsfor mixed-matrix membranes, because MMMscontaining nanoscopically small, thin nanosheetscan allow high separation performance at muchlower loading than that required for isotropicfillers. For example, 2D nanomaterials [i.e., thosewith one dimension on the nanoscale (e.g., MOFnanosheets and graphene oxide)], rather than0D [all three dimensions on the nanoscale (e.g.,carbonmolecular sieves, silica, andMOF crystals)]or 1D [two dimensions on nanoscale (e.g., carbonnanotubes and aluminosilicate nanotubes)] nano-materials, may be preferred because they can beincorporated into ultrathin membranes such asthe selective skin layers of thin-film compositeor hollow fiber membranes. MOF nanosheetsexhibiting high gas permeance and high gasselectivity (e.g., H2/CO2 separation) have beendeveloped (84). When such MOF nanosheets areincorporated into a polymer matrix, the resultingMMMs can improve gas separation performanceby eliminating nonselective permeation pathwaysas compared with isotropic MOFs. Rodenas et al.

compared the CO2/CH4 selectivity with MMMs,including a bulky-type MOF, nanosized MOF,and MOF nanosheets, based on the same MOFmaterial (85). Only MOF nanosheets in the MMMshowed improved selectivity and no significantpermeability loss relative to the neat polymermembrane. Similar effects can be observed inother nanosheet-incorporated MMMs. When GOnanosheets are incorporated into polyether-basedcopolymer membranes for CO2 separation, CO2/N2

selectivity increased significantly compared withthe pristine polymer membrane with no perme-ability penalty, even at low loadings (e.g., below0.1 weight %) (86).

Comparison of transport characteristicsof synthetic and biological membranes

Unlike synthetic membranes, biological mem-branes exhibit both high permeability and highselectivity. For example, the potassium ion chan-nel in cellmembranes is thousands of timesmorepermeable to potassium than sodium ions, despitethe smaller ionic (i.e., crystallographic) size ofsodium, and exhibits permeation rates (~108 ions/s)approaching the diffusion limit (87). Polymermembranes often exhibit little selectivity forions of like valence and transport such ions or-ders of magnitude more slowly. For example,McGrath et al. reported NaCl and KCl perme-ability coefficients of 3.8 × 10−8 cm2 s−1 and 4.4 ×10−8 cm2 s−1, respectively, in a di-sulfonatedpoly(arylene ether sulfone) membrane (88). KClpermeation was more rapid than NaCl permea-tion by a factor of ~1.2, whereas in potassium ionchannels, K+ is thousands of times more perme-able than Na+ (87, 89).Rates of K+ transport in ion channels may be

up to 108 ions/s (87). The diameter of the selec-tivity filter is approximately 0.3 nm, so the areaavailable for ion transport is 0.071 nm2. Thus, theK+ flux through the selectivity filter is 0.235 mol/(cm2 s). A typical extracellular K+ concentra-tion is 4 mM, and a typical intracellular K+

concentration is 155 mM (90). The length of theselectivity filter is 1.2 nm (87). On this basis, thepermeability coefficient of K+,PKþ, is estimatedas follows (39, 91): PKþ ¼ JKþL=DCKþ , whereJKþ is the flux of K+, L is the length of theselectivity filter, and DCKþ is the K+ concentra-tion difference between the extracellular andintracellular compartments. Thus, the K+ perme-ability of an ion channel,PKþ , is 1.9 × 10−4 cm2 s−1,~4 orders of magnitude faster than that reportedby McGrath et al.As a further comparison, the Na+ permeability

of a Nafion synthetic ion exchange membranewas calculated using data reported by Pintauroand Bennlon (92). The Na+ concentration inNafion equilibrated with a 1 M NaCl solutionwas 1.21mol L−1 (swollenmembrane). The diffusioncoefficient of Na+ in the membrane at the sameconditions was 2.62 × 10−6 cm2 s−1. The Na+ per-meability,PNaþ, was calculated using the solution-diffusion model (91): PNaþ ¼ Cm

NaþDNaþ=CsNaþ,

where CmNaþ is the Na+ concentration in the mem-

brane, CsNaþ is the Na+ concentration in the solu-

tion contiguous to the membrane (1M), andDNaþ

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Fig. 3. In designing mixed-matrix membranesto overcome the upper bound, compatibilitybetween filler and polymer, filler particlesize and shape, and homogeneous filler dis-tribution are important factors. (Case 1)Molecular sieving fillers (e.g., CMS and zeolites)often lead to selectivity increases and perme-ability decreases (35). (Case 2) Molecularsieving fillers with nano size or nanosheetshapes (e.g., MOFs nanocrystals or 2D nano-sheets) can improve both permeability andselectivity (55). (Case 3) Fillers with interfacialvoids, even when homogeneously dispersed,can result in increased permeability anddecreased selectivity (55).

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is the sodium diffusion coefficient in the mem-brane. Thus, the Na+ permeability in Nafion was3.1 × 10−6 cm2 s−1, nearly two orders of magni-tude lower than that of the potassium ion chan-nel, demonstrating the high permeability of ionchannels relative to synthetic membranes.In aquaporins, water can transport as fast as

~3 × 109 molecules/s through the water channel,whereas H3O

+ and small neutral solutes arealmost completely excluded (48, 93–95). Suchtransport properties are simply unattainablewith current synthetic membranes (68). Thesecombinations of high selectivity and permeationare ascribed to several common structural fea-tures in both aquaporins and potassium ion chan-nels: (i) uniform pore sizes of just the right size toaccommodate the desired ion or water molecule;(ii) hourglass-shaped pores, with a very shortselectivity filter [i.e., 12 Å long in the potassiumchannel (87) and ~20 Å in AQP1 aquaporin (93)],flanked by wider regions (i.e., vestibules) to accom-modate rapid ion or water transport to and fromthe selectivity filter; and (iii) exquisitely tunedmolecular interactions to energetically and en-tropically facilitate partitioning of desired spe-cies into the channel (87, 93).Direct incorporation of bacterial water chan-

nel proteins [aquaporin Z (AQP)] into syntheticmembranes can lead to improved combinationsof water transport and salt rejection in de-salination membranes. In 2007, Kumar et al.reported successful insertion of AQP proteinsinto synthetic triblock copolymer vesicles to formspherical cavities (~117-nm radius) with AQP unitsspanning the vesicle wall (96). The rate of watertransport through the vesicle walls increased 5to 10 times upon introduction of AQP. To createa functional membrane, AQP-containing vesicleswere ruptured onto a porous support membraneto form a planar bilayer, which acted as theselective barrier of the membrane (97). Suchmembranes generally exhibited low salt rejec-tion due to unavoidable defects. Another approachis to incorporate AQP-containing vesicles intothe aqueous diamine solution commonly usedto prepare NF and RO membranes by inter-facial polymerization (98). However, separationperformance of membranes prepared by thissimple approach is mostly dependent on thesurrounding polymer matrix, not on the aqua-

porin channels themselves. Although aquapor-ins have the potential to create highly permeable,salt-rejecting membranes, no studies to datehave demonstrated higher performance datafor aquaporin-based membranes than for state-of-the-art thin-film composite desalination mem-branes (48).Although some initial fouling and cleaning

data have been reported for aquaporin-basedmembranes (49), further exploration of the long-term robustness of such membranes in actualdesalination processes is needed. Examples ofsuch studies include fouling properties, toleranceto common membrane-cleaning chemistries, andstability of AQP-based membranes. Moreover,higher selectivity is needed to be competitivewith existing RO membranes. Depending uponits source, water slated for desalination can con-tain complex mixtures of ions and other com-ponents, some of which (e.g., mercury ions) areknown to disable water transport in aquaporins(93). Studies to date have mainly focused onsimple salts (e.g., NaCl), so the performance ofsuch membranes for separating other commonions, or mixtures of ions, is largely unknown.Ability to remove solutes such as boron and lowmolar mass neutral molecules, which are prob-lematic for existing RO membranes, has notbeen reported. Similar considerations will applyto other biomimetic membrane structures underdevelopment.

Design constraints beyond permeabilityand selectivity

Many studies focus exclusively on making mem-brane materials with better permeability and/orbetter selectivity. However, the ultimate perform-ance of a membrane is gauged by flux (or per-meance) and ability to separate mixtures ofpractical interest. High flux depends on usinghigh-permeability materials and making thinmembranes from those materials, which is whythe separating layer of current membranes isoften less than 100 nm thick. Making such thin,defect-free membranes on a large scale in areproducible fashion is a critical barrier to in-troduction of new membrane materials. Moreover,as discussed further below, not every separationdemands or even benefits from membranes withultrahigh permeability or selectivity. Additionally,

some applications cannot use or benefit fromhigher flux. To date, only a handful of familiesof polymers have been commercialized as sepa-ration membranes (3). High permeability is onecomponent of high flux but not the only one.To obtain high flux, one may design a materialwith a higher permeability coefficient, make anexisting membrane thinner, or increase the drivingforce for transport. However, there are limitationsand drawbacks to each of these approaches.Figure 4 shows cross sections of typical gas

separation and RO membranes. All membranesfor these applications are formed in solvent-basedprocesses that lead to a thin (~100 nm) selectivemembrane layer situated on a porous support,which provides mechanical strength to the thinselective membrane. This is about the thinnestthat can be achieved in large-scale membraneproduction processes with current procedureswithout introducing intolerable amounts ofpinhole defects (i.e., through pores) that allowselectivity-destroying bulk convective flow (74, 75).The porous support may be 50 to 200 (or more)mm thick and typically has surface porosity valuesin the range of 1 to 10%, with small surface pores(<100 nm) to provide a relatively smooth surfacefor the nonporous selective layer (99, 100).Figure 5A shows an example of the effect of

support mass transfer resistance on upper-boundperformance of a thin-film composite (TFC) gasseparation membrane consisting of a thin selec-tive separating layer on top of a porous support.Such membrane structures are widely used com-mercially because the separation layer thicknesscan be quite thin (~100 nm) and, in many cases,the support can be made from a low-cost, me-chanically robust engineering thermoplastic (e.g.,polysulfone). This approach allows one to usepotentially exotic, expensive materials for theseparating layer, because so little of this materialis used per square meter of membrane area thatthe overall cost of the membrane can be quitelow. However, if the thin selective layer becomesextremely thin (i.e., much less than 100 nm), thedistance a solute molecule must travel throughthe selective layer of the membrane to reach apore in the porous support can become greaterthan the selective layer thickness, and flux doesnot increase as expected with decreasing thick-ness. In gas separation membranes, addition ofa high-permeability, thin “gutter” layer betweenthe thin selective separating layer and the poroussupport helps mitigate this phenomenon, butsimply making thinner selective layers does notguarantee flux increases (99). Although the poroussupport is often assumed to contribute negligiblyto mass transfer resistance across a membrane (i.e.,all of the mass transfer resistance is due to thethin selective membrane itself), this approxima-tion becomes less and less valid as membranematerials become thinner and more permeable,leading to fluxes that do not increase as the thick-ness of the thin selective membrane decreases andselectivities that are far below intrinsic values ofthe separation material of interest (101). Thus,design of new membrane materials without con-sideration of membrane support properties can

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Fig. 4. Morphology of state-of-the-art membranes. Examples of (A) hollow fiber gas separationmembrane (118) and (B) flat sheet RO membrane (91).

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lead to performance much worse than that ex-pected based on results from free-standing films.Such support mass transfer resistance has beenrecognized, for example, to have pronouncedperformance-limiting effects in the current gen-eration of forward osmosis membranes (40)and has long been important in gas separationmembranes (99).In water purification membranes, RO de-

salination provides an example of the insignif-icance of high-permeability membranes on processefficiency. Numerous studies have suggested thatdeveloping high-permeance ROmembranes couldreduce energy consumption in desalination,which is proportional to the applied hydraulicpressure to drive water permeation across themembrane (1, 72, 96). However, energy consump-tion is constrained by the conventional single-stage operation of RO systems, in which theminimum hydraulic pressure, and hence theminimum specific energy (i.e., energy per vol-ume of product water), is equal to the osmoticpressure of the exiting brine (1, 102). Recentprocess modeling for RO seawater desalinationindicates that increasing membrane water per-meance from 2 L m−2 h−1 bar−1, the current levelof commercial TFC desalination membranes, to10 L m−2 h−1 bar−1, results in only a 3.7% re-duction in energy consumption (102). Moreover,a further 10-fold increase in permeance from 10

to 100 L m−2 h−1 bar−1 produces a meager 1.0%reduction in energy consumption. Similar con-clusionswere obtainedwhenmodeling RO brackishwater desalination (102). Although high-permeanceROmembranesmay have the potential to reducerequired membrane area, this solution will notbe practical because severe concentration polar-ization (CP) induced by the high water flux willsignificantly hinder process performance (1). Inaddition, membrane fouling, which is already amajor problem with current-generation mem-branes, is exacerbated at higher water fluxes(103, 104). Rather than increasing membranepermeance, increasing the water-solute selectivity(or minimizing solute passage) of ROmembranesshould be a very important goal for improvingprocess performance and yielding higher-qualityproduct water (48, 102). Current challenges withexistingmembranes include the removal of boronin seawater desalination,minimization of the pas-sage of low–molecular weight toxic contaminantsin water and wastewater reuse [e.g., arsenic,fluoride, and many uncharged solutes, such asendocrine disruptors increasingly found inwater(105)], and production of high-purity water forvarious industries withminimal deionization stepsafter the RO stage (102).Membrane separations are often limited by

available driving force, so increases in mem-brane material selectivity result in little or no

gain in product purity (3). In gas separation mem-branes, this concept is quantified by the pressureratio (i.e., the ratio of feed to permeate pressure)divided by membrane selectivity (3). Pressureratios may be set by economic considerationslargely dependent on process conditions (i.e.,independent of membrane properties). In gasseparation applications, typical pressure ratiosare 5 to 15 (106). Designing materials with se-lectivity values much greater than the pressureratio yields little or no improvement in productpurity, as shown in Fig. 5B. Membranes used inindustrial hydrogen separations (3) and thoseconsidered for postcombustion carbon capture,for example, have low pressure ratios, limitingthe need for highly selective membranes (106).Wessling and colleagues recently demonstratedthe use of upper-bound properties of membranescoupled with process modeling to identify eco-nomically optimal combinations of permeabilityand selectivity for nitrogen removal from naturalgas (107). Such studies for other gas and liquidseparations of interest would be desirable toprovide appropriate targets for materials design.In addition to having excellent transport prop-

erties, membranematerials must bemechanicallyrobust to survive manufacturing, installation, andlong-term use. For example, seawater RO mem-branes are routinely used at pressures of 55 bar,and gas separation membranes may operate at

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Fig. 5. Effect of membrane support and operating conditions onseparation characteristics of gas separation membranes. (A) Mem-brane support. (B) operating conditions. (A) shows the 2008 upper-bounddata for CO2/N2 separation translated into the selectivity and permeance(i.e., pressure-normalized flux) that could be achieved by placing a thin(100 nm) membrane onto a slow (103 GPU), medium (104 GPU), or fast(105 GPU) porous support membrane. For brevity, only 20% of the 2008upper-bound data have been shown on the selectivity-permeance plot. Thedashed lines indicate the expected performance of materials lying on theupper bound. The star [left side of (A)] denotes permeability/selectivity of

a hypothetical material with separation properties above the upper bound.The stars [right side of (A)] denote permeance and selectivity of thin-filmcomposite membranes of this material using different supports, showingthat a high flux support is needed to reach desirable performance (blueshaded region) for postcombustion CO2 capture (15). The procedure forgenerating the upper-bound lines in the selectivity-permeance plot isdescribed here (119). (B) shows the effect of varying membrane selectivityon permeate vapor concentration for a vapor separation membraneoperating at a feed/permeate pressure ratio of 20 and 1% vapor inthe feed.

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pressures exceeding 100 bar (3). High-salinitybrines (e.g., much greater than seawater, such aswater produced from hydraulic fracking) wouldrequiremechanicallymore robust ROmembranesto enable operation at ultrahigh pressures. Forexample, using the extremely saline water (34%salinity) from the Dead Sea would requiremem-branes operating at pressures ofmore than 250bar(108). Details of the mechanical property require-ments and design criteria, both for membranesand for their porous supports, are currently poorlyunderstood, in part due to the lack of mechanicalproperty data accompanying reports of newmem-brane materials.Membrane materials must also be chemically

and thermally tolerant to conditions encounteredduring operation. For example, oxidatively stable(i.e., chlorine tolerant) RO membranes remain anelusive goal. Such materials are needed becauseaqueous chlorine (e.g., hypochlorite) is widelyused to control biological activity in water streamsbeing fed to desalination processes, and currentaromatic polyamide–based polymers, the state ofthe art for desalination membranes, have poorchlorine tolerance (109). Polymeric gas separa-tion membranes are rarely deployed in applica-tions exceeding 100°C due to a lack of stabilityof such membranes at high temperatures. Sep-arations such as those found in precombustioncarbon capture could benefit from membraneswith much better thermal stability (110). Design-ing membranes that are resistant to plasticization(i.e., penetrant-induced swelling and subsequentloss of separation properties) will be required formembranes to be used in applications such asolefin/paraffin separation (36, 37). Most impor-tant, membrane materials must be scalable to bemanufactured in defect-free, large surface areas.

Outlook

Increasing demand for energy-efficient gas andwater separations, coupled with growing avail-ability of nanomaterials and a deeper under-standing of the structural features of biologicalmembranes that give them excellent permeabil-ity and selectivity, has stimulated substantialresearch aimed at overcoming the permeability/selectivity trade-off. Membranes in use todaywere discovered, in many cases, by serendipity.Molecular-level design and insight, includingadvanced simulation and modeling, will be crit-ical for breakthroughs going forward. For exam-ple, the approaches used to prepare membranestoday do not allow for independent control ofpermeation properties of interest [e.g., watertransport cannot be controlled independent ofsalt (or other solute) transport, and the transportof one gas, e.g., CO2, cannot be systematicallymanipulated without changing the transportof other gases, e.g., CH4], even though such pro-perties would be highly desirable. Whereas tra-ditional membranes for water and gas separationsare largely based on polymers and are subjectto the permeability-selectivity trade-off, manynew materials and design approaches (e.g., bio-inspired, biomimetic, or MMMs) offer the hopeof better control over pore size and size distri-

bution, which can break the conventional upperbound.However, many questions remain about both

new and existing membranes. For example, ourfundamental understanding of the basic thermo-dynamics and diffusion properties of water andions in polymers used in RO and electrodialysismembranes and many energy applications (e.g.,fuel cells, batteries, and reverse electrodialysis) isat an extremely rudimentary level (111), althoughrecent advances in this area are allowing forprediction of ion sorption and transport in highlycharged ion exchangemembranes (111, 112).Whiletheoretical models have been proposed for theupper bound for gas separation membranes (22)and desalinationmembranes (47), no such analogexists today for other separations, such as electro-dialysis, although the empirical evidence is over-whelming that such a trade-off exists (46). Thereis a real need for fundamentalmodeling, at lengthscales ranging from atomistic to continuum, toprovide rational guidance for designing futuremembranes. More recently developed nanomate-rials and MMMs would also benefit from anincreased focus on fundamental modeling. Inall cases, better understanding of structure-property-performance relationships in new, aswell as existing, membranematerials is urgentlyneeded.For all membrane materials, it is critical to

consider factors other than permeability andselectivity in materials design. Today, we typicallyuse rather elaborate, nonequilibrium, continuousprocesses involving large amounts of volatile,potentially toxic solvents to manufacture mem-branes. An advantage to this approach is thewidespread use of composite membranes, wherea thin (~100 nm) separating membrane is ap-plied to a porous support membrane, which canbe made of a relatively inexpensive engineeringthermoplastic. Such composite membranes allowthe use of novel, expensive materials as the sep-arating membrane, because so little of the sep-arating membrane is required for a given area ofmembrane. Nevertheless, novel processing strat-egies to simplify membrane manufacturing andscale-up would contribute remarkably to accel-erating deployment of new membrane materials.Development of solvent-free membrane manufac-turing processes or processes using environmen-tally benign, inexpensive solvents (e.g., water)would bring about disruptive, sustainable changesin membrane fabrication. Issues such as processconstraints, material processability, and long-termstability in the process environment where themembranes will operate should be built into re-search efforts to identify, as early as possible,materials that can be deployed for large-scale,practical challenges, such as the growing needfor clean water, treatment of waste products fromhydraulic fracturing, and climate change.

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119. The gas permeance of a thin film composite membrane, JC ,can be calculated using the series resistance model (10)1=Jc ¼ ‘A=PA þ 1=JB , where PA is the gas permeability (inunits of barrer) of the active layer, JB is the gas permeance (inunits of GPU) of the porous support, and ‘A is the thickness ofthe separation membrane (i.e., active layer). The permeance-selectivity data in Fig. 4A were calculated using this model.The CO2 permeance of the composite membrane wascalculated from JCO2

c ¼ ð‘A=PCO2A þ 1=JCO2

B Þ�1 and the N2

permeance of the composite membrane was calculated fromJN2c ¼ ð‘A=PN2

A þ 1=JN2B Þ�1. Finally, the selectivity, aCCO2=N2

, wascalculated from aCCO2=N2

¼ JCO2c =JN2

c . To demonstrate theimportance of the porous support layer, the N2 permeance ofthe porous support layer in Fig. 4A is varied over a range ofvalues (1000, 10,000, and 100,000 GPU) representing slow,medium, and fast support membranes, respectively.Assuming Knudsen selectivity in the porous support, the CO2

permeance of the porous support layer is then calculatedfrom JCO2

B ¼ JN2B

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiMN2

=MCO2

p ¼ 0:798JN2B , where MN2

is themolecular mass of N2, and MCO2

is the molecularmass of CO2. The dashed lines in the selectivity-permeanceplot in Fig. 4A were generated as described below.The upper-bound relationship for CO2/N2 is (23)PCO2

¼ 30; 967; 000ðaCO2=N2Þ�2:888. This equation was used

to obtain CO2/N2 selectivities for CO2 permeability valuesranging from 10−4 to 105 barrer. Subsequently, N2 perme-ability values were calculated from PN2

¼ PCO2=aCO2=N2

. Theselectivity and permeance values for the composite mem-branes were then calculated according to proceduresdescribed above.

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ACKNOWLEDGMENTS

We are grateful to many members of the membrane communityworldwide who contributed articles, advice, and perspectivesduring the preparation of this review. H.B.P and B.D.F.acknowledge financial support by the Korea CCS R&D Center(KCRC) grant funded by Ministry of Science, ICT, and FuturePlanning from the Korean government (grant 2016910057). Thework of J.K. and B.D.F. was supported by the Australian-American Fulbright Commission for the award to B.D.F. of theU.S. Fulbright Distinguished Chair in Science, Technology,and Innovation sponsored by the Commonwealth Scientific andIndustrial Research Organization (CSIRO); the Division ofChemical Sciences, Geosciences, and Biosciences, Office ofBasic Energy Sciences of the U.S. Department of Energy (grantDE-FG02-02ER15362); and the International Institute for CarbonNeutral Energy Research (WPI-I2CNER), sponsored by the WorldPremier International Research Center Initiative (WPI), MEXT,Japan. The work of J.K. was also sponsored by the NationalScience Foundation (NSF) Graduate Research Fellowship under grantDGE-1110007. The work of M.E. was supported by the NationalScience Foundation through the Engineering Research Center forNanotechnology-Enabled Water Treatment (ERC-1449500) and bygrant CBET 1437630. We also thank E. Zumalt and P. Wiseman forpreparing the graphic for the print summary.

10.1126/science.aab0530

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Maximizing the right stuff: The trade-off between membrane permeability and selectivityHo Bum Park, Jovan Kamcev, Lloyd M. Robeson, Menachem Elimelech and Benny D. Freeman

DOI: 10.1126/science.aab0530 (6343), eaab0530.356Science 

, this issue p. eaab0530Sciencehighlight cases where the challenges lie in areas other than improved separation performance.attempts to break past this upper bound. Some inspiration has come from biological membranes. The authors also

review the advances that have been made inet al.the selectivity, which limits the quality of the separation process. Park indicated that there was an upper bound on the trade-off between membrane permeability, which limits flow rates, and

Membranes are widely used for gas and liquid separations. Historical analysis of a range of gas pair separationsFiltering through to what's important

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